Originally a term for gypsies (corruption of egyption of which they are not). In today's PC world they would be called Roma. They choose to live in trailer (carvans). Funny they often do quite well financially and will build a fancy house to prove it...then they will park the carvan out front and live in it.
A tinkers dam was litterally a dam. They made a small clay dam around a hole in the pot before pooring in molten repair metal. After filling the dam would be brushed away as worthless, hence, not worth a tinkers dam.
They would typically do small odd jobs and thus if you are doing any small odd job, in modern usage it has become to tinker.